Leptophilic dark matter and the anomalous magnetic moment of the muon

We consider renormalizable theories such that the scattering of dark matter off leptons arises at tree level, but scattering off nuclei only arises at loop. In this framework, the various dark matter candidates can be classified by their spins and by the forms of their interactions with leptons. We determine the corrections to the anomalous magnetic moment of the muon that arise from its interactions with dark matter. We then consider the implications of these results for a set of simplified models of leptophilic dark matter. When a dark matter candidate reduces the existing tension between the standard model prediction of the anomalous magnetic moment and the experimental measurement, the region of parameter space favored to completely remove the discrepancy is highlighted. Conversely, when agreement is worsened, we place limits on the parameters of the corresponding simplified model. These bounds and favored regions are compared against the experimental constraints on the simplified model from direct detection and from collider searches. Although these constraints are severe, we find there do exist limited regions of parameter space in these simple theories that can explain the observed anomaly in the muon magnetic moment while remaining consistent with all experimental bounds.